Direct Torque Feedback for Accurate Engine Torque Delivery ... · torque feedback control has been proposed in the literature using either estimated or measured torques as feedback

Anwar AlkeilaniDepartment of Electrical and Computer

Engineering,

Wayne State University,

Detroit, MI 48202

e-mail: [email protected]

Le Yi WangDepartment of Electrical and Computer

Engineering,


Detroit, MI 48202


Hao YingDepartment of Electrical and Computer

Engineering,


Detroit, MI 48202


Direct Torque Feedback forAccurate Engine TorqueDelivery and ImprovedPowertrain PerformanceAt the present time, both control and estimation accuracies of engine torque are causesfor underachieving optimal drivability and performance in today’s production vehicles.The major focus in this area has been to enhance torque estimation and control accura-cies using existing open loop torque control and estimation structures. Such an approachdoes not guarantee optimum torque tracking accuracy and optimum estimation accuracydue to air flow and efficiency estimation errors. Furthermore, current approach overlooksthe fast torque path tracking which does not have any related feedback. Recently, explicittorque feedback control has been proposed in the literature using either estimated ormeasured torques as feedback to control the torque using the slow torque path only. Wepropose the usage of a surface acoustic wave (SAW) torque sensor to measure the enginebrake torque and feedback the signal to control the torque using both the fast and slowtorque paths utilizing an inner–outer loop control structure. The fast torque path feed-back is coordinated with the slow torque path by a novel method using the potential tor-que that is adapted to the sensor reading. The torque sensor signal enables a fast andexplicit torque feedback control that can correct torque estimation errors and improvedrivability, emission control, and fuel economy. Control oriented engine models for the3.6L engine are developed. Computer simulations are performed to investigate theadvantages and limitations of the proposed control strategy versus the existing strategies.The findings include an improvement of 14% in gain margin and 60% in phase marginwhen the torque feedback is applied to the cruise control torque request at the simulatedoperating point. This study demonstrates that the direct torque feedback is a powerfultechnology with promising results for improved powertrain performance and fueleconomy. [DOI: 10.1115/1.4033257]

1 Introduction

Design and control of internal combustion engines for automo-tive powertrain aims to achieve improved vehicle performance,including enhanced drivability, suppressed noise, vibration, andharshness, improved safety, increased fuel economy, and reducedemissions. Stringent governmental regulations on fuel economystandards and emission levels demand more sophisticated controlsystems that can balance these, often conflicting, performance cri-teria under diversified driving conditions and engine operatingpoints. One common interface signal for control systems forengine, transmission, emission, traction, and vehicle stability isthe engine brake or flywheel torque signal. These systems requirethe engine to calculate the desired torque and deliver the actualtorque with accuracy. The accuracy has two related aspects. Thefirst aspect is the accuracy of torque estimation, namely, the esti-mated engine brake torque compared to the true one. The secondaspect is the accuracy of tracking control in delivering therequested torque.

Throughout the recent history of automotive powertrain, specif-ically since the introduction of microcontrollers into engine man-agement systems, indicated and brake engine torques have beenestimated indirectly using models that incorporate readings fromvarious engine sensors. Sensors for the intake manifold absolutepressure (MAP) or mass airflow (MAF), exhaust gas oxygen con-tent (EGO), crank shaft speed, throttle position, inlet airflow tem-perature, engine oil temperature, etc. are examples of sensors that

are employed within torques estimation models. For example,gross-indicated torque is calculated as a function of the estimatedair charge trapped in the cylinders via a calibration lookup tableassuming unity torque (combustion) efficiency [1]. The air chargeitself is estimated on the basis of either the MAP or MAF [2,3].After the gross-indicated torque is calculated, it is adjusted totake into account the effect of torque efficiency changes based onspark angle, air/fuel ratio, percentage of ethanol, fuel shut off(FSO), exhaust gas recirculation, and any other parameters thatmay affect torque efficiency. The combined effect of such param-eters estimations introduces a challenging problem for high accu-racy. To calculate engine brake torque, the effects of all torquelosses that are also estimated from various calibration lookuptables need to be subtracted from the adjusted indicated torque.This includes estimation of friction, pumping losses, and lossesthat result from extra loads for driving various accessories.

Accumulations of the sensors’ measurement errors, modelinginaccuracies from model structures and calibrations, aging anddrift factors of engines as well as cylinder-to-cylinder combustionvariations have prevented developers from achieving optimumsolution [4].

The demand for better torque estimation and tracking controlincreased [5] with the introduction of the electronic throttle con-trol system or the “drive by wire” system that are torque-basedcontrol (as opposed to pedal-follower-based control). Transmis-sion clutch controls require accurate engine torque especially dur-ing shift operation. Engine stop start (ESS) systems also demandvery high torque accuracy levels in the first stages of engine start(typically within the first 350 ms). The required accuracy is diffi-cult to achieve with the current adopted estimation methodsmainly due to inaccuracies related to air charge and combustion

Contributed by the IC Engine Division of ASME for publication in the JOURNAL

OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 2, 2016;final manuscript received March 10, 2016; published online May 3, 2016. Editor:David Wisler.

Journal of Engineering for Gas Turbines and Power NOVEMBER 2016, Vol. 138 / 112801-1Copyright VC 2016 by ASME

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efficiency estimations during the short time period followingengine start.

This explains the significant amount of research activity toenhance torque estimation and measurement [4,6–10]. Withoutreliable direct torque measurement, robust torque feedback con-trol is challenging especially during transients. Research for usingtorque sensors in engine controls is gaining momentum due to theemergence of robust and cost-effective SAW technology and itsusage in fabricating torque sensor [11] that permits researchers toperform direct engine torque feedback control as well as otherfunctions. In Refs. [12,13], a torque sensor was used to performoptimum combustion phasing control. In Ref. [14], H1 controllerwas designed to close the loop on torque but using the throttleonly as an actuator. In Ref. [15], proportional integral (PI) control-ler was designed to close the loop on torque also using the throttleonly as an actuator. In these papers, fast torque request is not con-sidered and is not coordinated with slow torque request.

Seeking remedies to such estimation and tracking accuracyissues, this paper takes an alternative approach to utilize newlyconsidered sensors, introduced primarily for other purposes andareas such as on-board diagnostics, to be used for torque control.This approach will maximize the benefits from these sensors andjustify the potential added cost. This paper investigates utilizationof an additional SAW brake engine torque sensor to accuratelymeasure and control the engine brake torque to track both desiredengine brake fast and slow torque requests. The main innovativepart about this research is the utilization of the flywheel torquesensor to control and adapt fast and slow torque paths usinginner–outer loop control structure.

Section 2 of this paper discusses the development of the controloriented mean value engine model. It also includes a simplifiedtransmission and vehicle dynamics plant models. Section 3 detailsthe calibration and validation of the plant model showing varioussimulation traces compared with data obtained from a representa-tive vehicle. Section 4 lists a typical torque realization schemeshowing the necessary foundations for the proposed work. Section5 shows the basic adopted control structures and discusses the pro-posed control algorithms. Section 6 shows major relevant simula-tion results, and finally, Sec. 7 includes system analysis discussionfollowed by summary and conclusion.

2 Integrated Powertrain Models

The advantage of the control oriented model shown in Fig. 1 isto rapidly and iteratively develop new advanced control strategiesusing model in the loop environment. The results of the advancedcontrol strategies can be evaluated before building hardware andtherefore minimizing cost and improving efficiency.

The proposed integrated powertrain plant model consists ofthree main subsystems: (1) engine, (2) automatic transmission,and (3) vehicle dynamics. The engine subsystem is broken downinto four subsystems: (1) throttle body, (2) engine breathing, (3)torque generation, and (4) crankshaft dynamics. The automatictransmission subsystem consists of two main parts: (1) torque con-verter and (2) gear box. In Secs. 2.1–2.3, we discuss these subsys-tems in detail.

2.1 Engine Plant Model. The modeled engine is a V6 3.6Lengine with dual variable valve timing. The engine plant modelconsists of the following submodels.

2.1.1 Throttle Body Model. The model of the throttle bodythat consists of a dc motor driving a throttle plate with a preloadedreturn spring and a set of gear trains is based on Ref. [16]. Theinput to the throttle body model is the pulse width modulation(PWM) duty cycle DCPWM that is applied on the voltage supplyVs, feeding the throttle body DC motor to control its output,namely, the throttle angle, uthr. The DC motor is connected to thethrottle plate shaft via two sets of reduction gear trains. Hence,knowing the total throttle gear ratio, GRthr, one can always relate

the angular speed of the motor xm (rad/s) to the angular speed ofthe throttle plate shaft xthr (rad/s) via

xthr ¼xm

GRthr

(1)

The throttle body model can be divided into an electrical modeland a mechanical model. The electrical model captures the first-order dynamics of the equivalent armature RL circuit of the DCmotor

DCPWM � Vs � Ra � ia � Vemf ¼ La

diadt

(2)

where Vemf¼xthr�Kme is the back emf voltage, Kme is themotor’s back emf constant (V s/rad), xthr is the throttle plateangular velocity (rad/s), uthr is the throttle plate angle (rad),DCPWM is the controller duty cycle of the PWM signal (%), Vs isthe throttle body DC motor supply voltage (V), Ra is the DCmotor’s armature equivalent resistance (X), ia is the currentthrough the DC motor’s armature (A), and La is the DC motor’sarmature equivalent inductance (H).

The mechanical part of the electronic throttle body (ETB) modelconsists of a safety spring with spring constant KS. The spring hastwo advantages: (1) when the spring is at rest, the throttle angle hasan opening (between 6 deg and 9 deg) to guarantee an elevatedengine speed in case of ETB power loss or malfunction so that thevehicle remains drivable. (2) The spring can return the throttle plateto its rest position in case of malfunction or power loss during largethrottle openings. The mechanical part of the model is derived fromthe torque-balancing equation. The net torque is the applied torqueby the DC motor excluding all torque losses, such as damping andfriction torques. This is captured by using the following second-order ordinary differential equation (ODE):

JETB

d2uthr

dt¼ Tm � Kbxthr � Tfsgn xthrð Þ � fn1 uthr;Ksð Þ

� fn2 uthrð Þ (3)

where JETB is the equivalent total inertia of the ETB,Tm¼Kmt� ia is the DC motor applied torque (N �m), Tf is thefriction torque (N �m), Kmt is the motor torque constant (N �m/A),xthr is the directional angular speed of the throttle plate (rad/s), Kb

is the DC motor’s viscous friction damping constant (N �m s/rad),Ks is the spring constant (N �m/rad), Sgn(xthr) is the signum func-tion, fn1ðuthr;KsÞ is the spring torque function (N �m), andfn2ðuthrÞ is the spring preloaded torque function (N �m).

fn1ðuthr;KsÞ is related to the throttle angle which is directlyrelated to the spring position. Depending on whether or not thespring is compressed or stretched, fn1ðuthr;KsÞ is given by

fn1ðuthr;KsÞ ¼Ksuthr if uthr > ujrest angle

0 if uthr ¼ ujrest angle

�Ksuthr if uthr > ujrest angle

8>><>>: (4)

fn2ðuthrÞ is related to the constant spring preloaded torque TPL

(N �m) and it is given by

fn2ðuthrÞ ¼TPL if uthr ¼ umin or uthr ¼ umax

0 else where

�(5)

Sgn(xthr) is defined by

sgnðxthrÞ ¼�1 if xthr < 0

0 if xthr ¼ 0

1 if xthr > 0

8<: (6)

112801-2 / Vol. 138, NOVEMBER 2016 Transactions of the ASME


2.1.2 Engine Breathing Model. This model is based on theintake manifold filling and emptying dynamics [5,17] given by

dmair m

dt¼ _mair thr �

Xtotal cyls

i

_mair cyl;i (7)

where i is the cylinder index, dmair m=dt is the air mass variationin the intake manifold (g/s), _mair thr is the mass flow rate of airpassing through the throttle (g/s), _mair cyl;i is the mass flow rate ofair in a given individual cylinder i (g/s), and total_cyls is theengine’s total number of cylinders.

In-flow model through the main throttle ( _mair thr) is based onquasi-steady state model [18,19] of flow through restriction orificegiven by the following piecewise function:

_mair thr

¼

CDApoffiffiffiffiffiffiffiffiRTo

p Prð Þ1c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2c

c� 11� Prð Þ

c�1c

� �sif pr >

2

cþ 1

� � cc�1

CDApoffiffiffiffiffiffiffiffiRTo

p c1=2 2

cþ 1

� � cþ1

2 c�1ð Þpr �

2

cþ 1

� � cc�1

8>>>>><>>>>>:

(8)

where po is the pressure upstream of the throttle (throttle inletpressure or sometimes called TIP) (kPa), pm is the intake mani-fold pressure (kPa) downstream the throttle (throttle outlet pres-sure or sometimes called TOP), and pr is the pressures ratio(pm/po), of downstream to upstream of the throttle pressures and

when pr � ð2=ðcþ 1ÞÞc

c�1, this is called sonic or chocked case. cis the ratio of specific heat capacities (cv/cp) of inlet air, cv isthe specific heat capacity at constant volume, and cp is the spe-cific heat capacity at constant pressure, and c is a function oftemperature and molecular constituents of inlet air (gas compo-sition). For example, for fresh air c¼ 1.4 at T¼ 250 K andc¼ 1.309 at T¼ 1500 K.

Once the throttle angle uthr is determined, the throttle cross-sectional area can be calculated using geometry. CD is thethrottle discharge coefficient that is empirically determined bymeasuring the throttle mass air flow rate at the sonic orchocked case [18]. Cd is meant to correct for the assumptionthat the flow through the throttle is isentropic flow. Typically,the combined term CdA is determined as a whole [20] by fit-ting the throttle airflow data using Eq. (8) and the fitting coef-ficients ax within CdA that is as a function of the throttleangle, uthr given by

Fig. 1 Illustration of integrated models used in this work

Journal of Engineering for Gas Turbines and Power NOVEMBER 2016, Vol. 138 / 112801-3


CdA ¼ a1 � u5thr þ a2 � u4

thr þ a3 � u3thr þ a4

� u2thr þ a5 � uthr þ a6 (9)

For the out-flow model, the outgoing flow from the intake mani-fold into the cylinder, _maircyl;i ðg=sÞ, can be written based on thespeed density equation derived from the ideal gas law as

Xtotal cyls

i

_mair cyl;i ¼gvqairVdN

2(10)

where gv is the engine volumetric efficiency (unitless), qair m isthe density of intake air inside the intake manifold (g/L), N is theengine speed (rev/s), and Vd is the engine displacement (L).

Since gv is a function of manifold pressure MAP, enginespeed N, and intake and exhaust CAM positions (intake centerline (ICL) and exhaust center line (ECL), respectively), Eq. (10)is rewritten such that

Ptotal cylsi _mair cyl;i ¼ f ðN;MAP; ICL; ECLÞ

and collected engine data are fitted to come up with an expressionforPtotal cyls

i _mair cyl;i. The final fitted model took the form of

Xtotal cyls

i

_mair cyl;i ¼ f ðN;MAP; ICL; ECLÞ

¼ b1þ b2�MAPþ b3� MAP2þb4�MAP3

þ b5�Nþ b6�N2þ b7�N3þ b8�N4

þ b9�MAP�Nþ b10� ICLþ b11� ICL2

þ b12� ICL3þ b13�ECLþ b14� ECL2

þ b15� ECL3þ b16� ICL�Nþ b17�ECL�N

(11)

where bx is the fitting coefficients of the least square estimate thatis used.

Finally, from the ideal gas law principle and from Eqs. (7)–(9)and (11), we have a first-order ODE with a single time constantK ¼ RsIAT=Vm, given by

_MAP ¼ Kdmair m

dt(12)

where Rs ¼ 287:058 ðJ kg�1 K�1Þ is the specific gas constant ofair, IAT is the inlet air temperature (K), and Vm is the intake mani-fold volume (m3).

2.1.3 Torque Generation Model. The engine brake torque iscalculated based on models of the gross-indicated engine torqueand engine torque losses [21]. The gross-indicated torque ismainly a function of the total engine cylinder air charge, CAC

CAC ¼ 2

Xtotal cyls

i

_mair cyl;i

N(13)

The gross-indicated torque at full efficiency, TG Indjfull eff ; is deter-mined without considering the effects of spark advance delta fromthe maximum brake torque (MBT) spark and deviation of air/fuelratio away from the lean best torque (LBT) air/fuel ratio. There-fore, the CAC data that are collected at the MBT spark and air/fuel ratio at LBT are fitted using the structure

TG Indjfull eff ¼ c1 þ c2 � CACþ c3 � N þ c4 � CAC2

þ c5 � CAC� N þ c6 � N2 (14)

where cx is the fitting coefficients from the least squares estima-tion. Using N in the fitting reduces modeling errors.

The effect of spark advance is captured by introducing sparkefficiency function, gspk. This efficiency is calculated by fittingtorque ratio data at different engine load levels (CAC). Thenumerator of the ratio is torque that resulted when spark advanceis modified from MBT spark. The denominator of the ratio is thetorque that results when the spark is at the MBT (best efficiency)

gspk ¼ s1 þ s2 � SADþ s3 � CACþ s4 � SAD2 þ s5

� SAD� CACþ s6 � CAC2 (15)

where sx is the fitting coefficients from the least squares estima-tion, and spark advance in degrees (SAD) (CAD) is the sparkadvance delta away from the MBT.

Similarly, the effect from air/fuel ratios can be captured byintroducing a lambda efficiency function, gaf. This efficiency iscalculated by fitting torque ratio data. The numerator of the ratiois the torque that results when the air/fuel ratio is perturbed awayfrom the LBT air/fuel ratio. The denominator of the ratio is thetorque that results when air/fuel ratio is at LBT air/fuel ratio

gaf ¼ l1 � LBTD3 þ l2 � LBTD2 þ l3 � LBTDþ l4 (16)

where lx is the fitting coefficients from the least squares estimationthat is used. Lean best torque delta (LBTD) is the air/fuel ratiodelta away from LBT air/fuel ratio

TG Ind ¼ TG Indjfull eff � gspk � gaf � gFSO (17)

where gFSO is the torque efficiency associated with the cylinderFSO defined as the percentage of turned-off fuel injectors to thetotal number of cylinders of the engine. Engine torque losses arederived by combining the effects of engine mechanical frictionand pumping losses for a fully warmed-up engine. The combinedlosses take the form

TLosses ¼ f1 þ f2 � N þ f3 �MAPþ f4 � N �MAPþ f5

�MAP2 þ f6 � N2 (18)

where fx is the fitting coefficients from the least squaresestimation.

The instantaneous brake torque, TI_Brake(t), is given by

TI BrakeðtÞ ¼ TG IndðtÞ � TLossesðtÞ (19)

This torque does not include any dynamics related to combustiondelay and the time it takes for the torque to actually act on theengine shaft. To capture these effects, a variable transport delay isadded such that

TBrakeðtÞ ¼ TI Brakeðt� tdðtÞÞ (20)

where TBrake(t) is the final engine brake torque, and td(t) is thevariable torque production delay given by

tdðtÞ ¼ 1=N (21)

2.1.4 Crankshaft Speed Dynamics. The second-order torque-balancing differential equation is used to calculate the enginespeed

Jeid2hdtþ Cei

dhdtþ Keih ¼ TBrake tð Þ – TLoad (22)

where h is the crankshaft position (rad), ðdh=dtÞ ¼xe is the angu-

lar speed of the engine’s crankshaft (rad/s), ðd2h=dtÞ ¼ ðdxe=dtÞ¼ ae is the angular acceleration of engine’s crankshaft (rad/s2), Jei

is the equivalent moment of inertia of the engine and transmissionimpeller (N �m s2/rad), Cei is the engine’s and transmission



impeller’s damping coefficient or rotational friction (N �m s/rad),and Kei is the stiffness of engine and transmission impeller’s orcoefficient of torsion (N �m/rad). TLoad (N �m) is the engine exter-nal load torque that comes from transmission impeller torque.This will be discussed in Sec. 2.2.

2.2 Automatic Transmission Plant Model. The transmis-sion model consisted of the two submodels: (1) torque convertermodel and (2) transmission gear box model that are explainedbelow.

2.2.1 Torque Converter Model. A torque converter consistsmainly of an impeller connected to the engine and a turbine that isconnected to the transmission input shaft. Both the impeller andturbine have speeds and torques associated with them. Fleming[6] described a basic model for a torque converter that is used asbasis in this section. The external load torque on the engine, TLoad,is the impeller torque, TImp

TLoad ¼ TImp ¼N

K

� �2

(23)

where the K factor is determined by fitting speed data and isdefined as a function of the ratio of the turbine speed, NT, to theengine speed, N

K ¼ fNT

N

� �(24)

NT is given in Sec. 2.2.2. The turbine torque, TT, is given by

TT ¼ gNT

N

� �� TImp (25)

2.2.2 Transmission Gear Box Model. The transmission gearbox consists of an input shaft and output shaft connected by gearsets. Turbine speed, NT, is the same as the transmission inputspeed, Nin, and is calculated from the equation

NT ¼ Nin ¼ Rgear � Nout (26)

where Rgear is the transmission gear ratio based on the currentgear. Nout is the transmission output speed given by

Nout ¼ Spdw � FDR (27)

where Spdw is the vehicle wheel speed (rpm) derived from thevehicle model as shown in Sec. 2.3, and FDR is a constant for thevehicle’s final drive ratio.

The transmission input shaft torque, Tin, is the same as theturbine torque TT. The transmission output shaft torque Tout isgiven by

Tout ¼ Rgear � Tin (28)

A simple transmission shift schedule as a function of the accelera-tor pedal position and vehicle speed (VS) with switching hystere-sis is implemented.

2.3 Vehicle Dynamic Model. This model calculates VS. It isbased on the torque-balancing equation similar to the crankshaftspeed dynamics model that was discussed previously. However, afirst-order differential equation is used for simplification. The nettorques involved here are the wheel torque, Tw, and the load tor-que, Tl. The wheel torque is derived from the transmission outputshaft torque based on FDR, using the equation

Tw ¼ Tout � FDR (29)

The load torque consists of three main components: (1) the dragand road–tire friction component, (2) the road grade load compo-nent, and (3) the braking load from the applied brake pedal

Tl ¼ f1ðVSÞ þ f2ðVS; hrÞ þ TBP (30)

where the function f1 of VS represents the drag and road–tire fric-tion load torque component of the load torque; f2 is a function ofVS and the road grade angle, hr (deg); and TBP is the braking tor-que applied by the driver’s brake pedal (N �m).

The final torque-balancing equation around the vehicle’swheels is given by

Jvav ¼ Tw � Tl (31)

where Jv is the vehicle’s inertia (N �m s2/rad), and av is the vehi-cle angular acceleration (rad/s2) from which the linear VS (mph)can be calculated given the tire radius, Rt (ft), using the followingODE:

_VS ¼ 120pRt Tw � Tlð Þ5280Jv

(32)

3 Plant Model Calibration and Validation

Starting from a high fidelity model established previously byGT-power (Gamma Technologies Software modeling tool forengine simulations which is an industry standard and part of theGT-SUITE software simulation tool for complete vehicle simula-tion), a complete engine grid mapping design of experiment(DoE) is established for the entire space of possible engine operat-ing points. Operating point is defined as a specific engine speedand engine brake torque condition. Figure 2 shows the space ofoperating points (one test per covered operating point) that areexercised.

Steady-state data are collected at each engine operating pointfor 30 s and averaged. The data are used to fit Eqs. (9), (11),(14)–(16), (18), (24), (25), and (30) describing the steady-statebehavior of the engine. The numbers of tests or operating pointsare around 1300 points. The following plots in Figs. 3–8 showthese tests and the results of the steady-state fitting.

To capture the transient effects of the engine, the constants ofthe ODEs (2), (3), (12), (22), and (32) are adjusted in order to fitthe transient model behavior with real engine data collected previ-ously from a real vehicle. The constants are initially set totheir nominal values based on the physics or specification butthen adjusted slightly for model accuracy. The following plots inFigs. 8 and 9 show the final validation of the main model state andoutput variables for a driving cycle.

4 Typical Torque Realization Schemes

A vital function of the engine torque management subsystem isthe torque realization. This implies that various engine’s actuatorshave to be coordinated to deliver the final requested torque. Thefinal requested torque can be delivered either via a slow torquepath or fast torque path. The torque requestors are arbitrated sepa-rately within these two separate torque domains.

The slow torque path request is related to air charge manage-ment via the throttle control and/or intake valves control. The fasttorque path request is related to spark advance control and/or FSOcontrol. The various torque requestors decide the path of the tor-que. Slow torque request can be used to increase or decrease theamount of torque delivered by the engine. It is referred to as slowpath because there is an inherent significant delay (relative delaywhen compared to fast path) due to intake manifold filling andemptying dynamics (breathing process of the engine).

The fast path torque request is referred to as fast because torquecan be delivered via spark adjustment and/or fuel injector



activation/deactivation almost instantaneously (some delay in theorder of fraction of engine cycle can be expected). The fast pathtorque request is typically used to reduce torque during torqueintervention from the various requestors, such as transmission

shift. During speed change phase, the transmission requests a spe-cific fast engine torque in order to improve shift response. Afterengine response to the request, the torque can be increased to itsoriginal level prior to the transmission torque request that the slow

Fig. 2 Space of DoE selected for engine data mapping

Fig. 3 Steady-state fitting of indicated torque and the error of fitting

Fig. 4 Steady-state fitting of cylinder MAF and the error of fitting



path would have delivered. This torque level is often referred to aspotential or feasible torque. This potential or feasible torque canbe approximated as a delayed or filtered version of the slow torquerequest slow. FSO control is another form of fast path, it turns offthe fuel completely in one instance for a given engine’s cylinder.The same process is applied to the rest of the cylinders sequen-tially (if needed based on the requested torque level) in a givenpattern related to firing order at a given rate. FSO control can alsobe used to modify the fraction of injected fuel amount in each

Fig. 6 CdA data fitting

Fig. 5 Steady-state fitting of cylinder torque losses and fitting error

Fig. 8 Pedal and brake inputs and modeled versus measuredvalues of MAP, transmission turbine speed, and VS

Fig. 7 Fitting of air-fuel ratio and spark efficiency data



cylinder to achieve certain torque levels based on torque effi-ciency. This approach is not common due to emission effects.

All of the slow torque requests from various requestors getcompared according to their magnitudes and priorities to deter-mine the final slow torque request. Based on the final slow torquerequest, a desired engine air charge is then calculated based on thedesired slow torque request through quasi-steady state generatedengine mapping data. This desired air charge is then convertedinto a desired mass air flow to be achieved by controlling the elec-tronic throttle position. The throttle model is based on compressi-ble flow equation through a restriction or an orifice [18].Essentially, these processes are the inverse models when com-pared to the models discussed previously in the engine plantmodel section. A feedback controller is often employed [2] that

utilizes the estimated air charge, acquired from models that usesensors such as MAF or MAP to close the loop on the errorbetween the estimated air charge and desired air charge. Thedesired throttle position itself is also controlled via feedback onthe actual throttle position. The same closed-loop concept isapplied to the variable valve timing actuator positioning control.Figure 10 illustrates the existing feedback loops (in black signalcolor) related to the slow torque path realization.

As shown in Fig. 10, there is no feedback loop performed ontorque explicitly. The existing direct feedback loops involve onlyair and fuel feedback controls. For the air, throttle and/or variablevalve timing is/are used to close the loop on desired engine massair flow. On the other hand, fuel metering depends on the amountof air charge inducted by the engine. Closed-loop fuel control isemployed using feedback from heated exhaust gas oxygen(HEGO)/universal exhaust gas oxygen (UEGO) sensors to main-tain the air fuel ratio target, typically near the stoichiometric airfuel ratio for nonlean burn gasoline engines.

Once the final fast torque request is determined from fast torquearbitration, it is converted into a desired torque efficiency. Using thedesired torque efficiency, the spark and FSO are adjusted based oncalibration tables without feedback to deliver the fast desired torque.There are several other schemes that can generate the requestedspark advance and FSO separately. These schemes are, however,beyond the scope of this paper. The aforementioned calibration ta-ble describing the relationship between the torque efficiency anddelta spark away from the MBT spark is highly nonlinear and diffi-cult to acquire as can be seen from the graph depicted in Fig. 7.

Fig. 9 Modeled versus measured values of transmission gear,engine speed, throttle, and engine brake torque

Fig. 10 Illustration of existing control loops and proposed one

Fig. 11 Raw SAW torque sensor reading and processed one



5 Algorithms and Cascading Control Structure

The SAW torque sensor measures the instantaneous enginebrake torque pulsations [11]. As a result of that, and since allengine torque requestors specify their torque demands as meantorque signal, the sensor output has to be processed to create anaverage signal.

In addition, the sensor output signal is processed to compensatefor the zero torque level offset as shown in Fig. 10. The offsetcompensation is needed since the sensor outputs are not zero atzero torque level. The value is found to be around 12 N �m.

Figure 11 shows a typical raw SAW torque sensor output wave-form and its average over one engine cycle with zero torque leveloffset compensation. Data are collected in a city driving condi-tion. Figure 12 shows a three-engine cycle during neutral engineidling. As shown, the processed torque sensor signal is close to0 N �m as expected.

Figure 13 shows the processed sensor torque as well as theengine control unit estimated torque superimposed with the finalrequested torque. It shows the difference between the sensor read-ing and the estimated engine torque especially in the negative re-gime and near zero torque levels.

Two controllers are suggested in this paper. One for the slowtorque control path (air path) and the other is for the fast torquecontrol path (spark advance and FSO). The two controllers usedfor this work are discrete proportional integral derivative (PID)controllers with variable gains as a function of the torque errorbetween sensed and requested engine torque.

For slow torque requests, the existing feed-forward term isadjusted by adding correction term from the new proposed torquesensor feedback loop. From that point of view, the system is a sin-gle input–single output system.

For torque requestors that utilize the fast torque path such astransmission torque requests, the spark advance and/or FSO isadjusted to ensure torque tracking accuracies. This is accom-plished by adding a correction term to the existing feed-forwardbased on feedback from the torque sensor.

During fast torque path closed-loop control activation uponreceiving a fast torque request, the slow torque path control loopis prevented from updating its feedback term in order to allow thefast torque path to handle the feedback torque control. This meansthat the two paths operate one at a time based on the type of thetorque request and when control authority is reached for one pathin which case the other path can be utilized to complement theperformance of the restricted one. For example, if there is a slowtorque reduction request and the throttle reaches its minimumlimit, then the fast path can be enabled to operate and adjust itscontrol parameters to reduce the error. This way fuel efficiency ismaximized.

Alternatively, the slow path torque feedback can still be madeto be active all the time by closing the loop on the potential torqueinstead of the actual torque only during fast torque requests. Thisway the actual torque can be used as a feedback on the fast pathand the potential torque can be used as feedback on the slow path.Potential torque (estimated) should equal actual torque when thereis no fast torque request intervention. This means actual torquecan adapt potential torque such that potential torque tracks theactual torque when there is no fast torque request. When a fast tor-que request is made, potential torque stops being adapted and getsused in lieu of the actual torque within the slow torque path andthe actual torque gets used as a feedback within the fast torquecontrol path. Any time a control actuator reaches its limits, aproper integral antiwindup strategy is invoked. It is found that

Fig. 12 Three engine cycles zoomed-in view of SAW torque sensor reading and processedone during neutral engine idling

Fig. 13 Requested engine brake torque, engine control unit esti-mated one as well as the signal as measured by SAW torque sensor



faster tracking is achieved by resetting the integral gain each timea new torque requestor changes.

As shown in Fig. 14 at any given stable operating point andbased on a sustained integral term (I-term), a portion of the I-termis off loaded from the I-term into an adaptive keep alive memoryto be used every time this operating point is revisited again. Thelogic used is similar to that described in Ref. [22]. This adaptiveterm is binned in either accessory load torque or friction torquedepending on whether or not an accessory load is activated inorder to enhance torque losses model. This is a clear advantage ofclosing the loop on torque as without this scheme, this can only bedone during idle control.

6 Simulations and Results

Simulations of combined plant and controllers models areimplemented using MATLAB

VR

and SimulinkVR

. The model issimulated two times to generate two sets of data that are superim-posed and plotted in the graphs shown below. The first set (desig-nated by the red-colored plots) serves as a baseline forcomparison purposes to compare the existing control scheme as aknown reference with the new one. The second data set (desig-nated by the blue-colored plots) is generated from the new pro-posed strategy. The baseline strategy performs open loop controlfor the desired brake torque, whereas the new proposed strategy

performs an explicit feedback control on the brake torque on topof the existing open loop feed-forward control. In order to appre-ciate the potential advantages, it was decided to test it in cruisecontrol mode. The simulations are focused on three main areas:(1) the performance of VS tracking when cruise control isengaged, (2) disturbance rejection capabilities when disturbanceis injected, and (3) transients’ performance when driver steps onthe accelerator pedal. The test scenario is designed such thatdriver gas pedal is depressed as a step input from engine idlecreeping VS at time t¼ 10 s. Once the VS reached around 62 mph,the driver gas pedal is let go at time t¼�17 s and �18 s causingthe vehicle to coast down up until VS reached 50 mph upon whichcruise control is engaged. When VS is maintained by the cruisecontroller, a disturbance is injected by simulating a steep hillmimicking a 4% grade. With the new proposed inner torque-basedloop, aggressive calibrations of the cruise control speed-basedouter loop are utilized. Simulations showed that the VS trackingperformance is improved while at the same time better torquetracking is realized. Disturbance rejection is also significantlyenhanced. The sample and execution times of these loops had tobe chosen such that an outer loop runs at a slower rate than aninner loop to ensure stability and control robustness.

It is important to note that the plot in Fig. 15 shows that for agiven driver pedal input, the VS in the system that utilizes closed-loop torque feedback control is higher than the system that runsonly open loop torque control for the same pedal. This means thatthe driver has to step more on the pedal in the case of the openloop torque to get the same result with closed-loop torque system.Such closed-loop torque control system can aid in enhancingpedal feeling experience by customers.

Figure 16 shows simulation results upon activating and engag-ing cruise control at 50 mph set-point just right after a period ofvehicle deceleration due to foot off the pedal. The simulations arerun for the existing strategy and the newly proposed one with tor-que feedback. The cruise control controller gains are kept thesame for the two strategies. Torque feedback not only enhancedthe torque tracking error by more than 20 N �m during torquesteady state but also improved VS tracking error as well.Fig. 15 Plots of initial vehicle launch simulation

Fig. 16 Plots of activation of cruise control simulation usingthe same cruise control gains for the two strategies

Fig. 14 Illustration of torque adaption areas



Figure 17 shows simulation results for testing the capability ofrejecting disturbances when a 4%-slopped hill is injected at themoment when the VS error is zero. Cruise control gains are keptthe same between the two strategies. There is no significantimprovement in disturbance rejection when cruise control control-ler gains are kept the same.

However, Figs. 18 and 19 show simulation results for the sametest scenarios as the ones shown in Figs. 16 and 17, respectively,but with utilization of aggressive cruise control controller gainsonly for the newly proposed strategy with torque feedback con-trol. These aggressive gains are possible because of the utilizationof the inner torque control loop. Without the proposed inner tor-que control feedback loop, the utilization of aggressive cruise con-trol controller gains will cause unacceptable drivability andcontroller performance issues, such as excessive VS overshootsand undershoots. These aggressive gains utilized in the newly sug-gested control strategy clearly improved VS tracking and enabledbetter disturbance rejection.

7 System Analysis

This section shows that the addition of an inner feedback con-trol loop for torque feedback (green signal line in Fig. 10) enhan-ces the gain and phase margins of the existing VS control whenclosing the outer feedback loop on VS. This analysis will befocused on the slow torque path since the cruise control is handledtypically by the slow torque path request. The idea here is to com-pute two total open loop transfer functions (without closing theloop on VS) with and without the torque feedback to compare thegain and phase margins for these two options. To do this,the system needs to be linearized around the equilibrium operatingpoint at which simulations are run. This equilibrium pointis, namely, VS¼ 50 mph, N¼ 1520 rpm, MAP¼ 40 kPa, andTHR¼ 0.22 V.

By observing Fig. 20, the transfer functions G1 and G2 need tobe calculated. G1 maps the input throttle to VS. G2 maps the input

throttle to engine brake torque. The transfer function of the con-troller C0 is 1=G2.

For the purpose of performing torque control in general and forthis analysis, G2 is set equal to G2. G2 is the plant itself and canchange overtime (due to component aging, drifting, etc.), whereas

Fig. 18 Activation of cruise control simulation results withaggressive cruise control gains for the proposed strategy

Fig. 19 VS and engine brake torque with hill disturbance injec-tion during cruise control with aggressive cruise control gainsfor the proposed strategy

Fig. 17 VS and engine brake torque with hill disturbance injec-tion during cruise control, while cruise control gains are keptthe same between the two strategies



G2 is chosen to be fixed and set to be equal to the nominal valueof the plant G2. C1 is the new proposed controller (PID) understudy, and C2 is an existing cruise control feed-forward controllerthat is typically a function of commanded VS and current enginespeed.

By defining the following succinct vector notation:

x ¼x1

x2

x3

24

35; where x1 :¼ MAP; x2 :¼ N; and x3 :¼ VS

u: is the THR (for the slow torque control system only)

y ¼ y1

y2

� ; where y1 :¼ VS and y2 :¼ TBrake

Then combining the developed plant model equations providedpreviously, one can write the following lumped two system non-linear differential equations:

_x ¼ f ðx; uÞ (33)

y ¼ gðx; uÞ (34)

where f is a function mapping R3 X R1 ! R3, and g is a functionmapping R3�R1! R2: x � R3, u � R1, and y � R2.

The rest of the system inputs such as spark, air/fuel ratio, gear,etc. are treated as known disturbances and their values at the equi-librium point are used in the equations. By using the Jacobian lin-earization method, the linear time invariant system matrices forthe two outputs are calculated as in the following expressions:

A :¼ @f

@x

x ¼ �xu ¼ �u

B :¼ @f

@u

x ¼ �xu ¼ �u

C :¼ @g

@x

x ¼ �xu ¼ �u

D :¼ @g

@u

x ¼ �xu ¼ �u

For G1, clearly the first row of the matrices C and D is [0 0 1] and[0], respectively, because the output y1 for G1 is the state VSitself.

For G2, the output y2 which is TBrake is a linear combination ofthe system state variables and input. Hence, the second row of Cand D matrices is determined by the expressions

C :¼ @TBrake

@x

x ¼ �xu ¼ �u

D :¼ @TBrake

@u

x ¼ �xu ¼ �u

Finally, the transfer functions G1 and G2 are found using: C(sI�A)�1 BþD.

From Fig. 20, the overall open loop (without the VS feedback)transfer function of the newly proposed system (with torque feed-back) is given by

HCL ¼ C1C2G1 �C1G1 C2C1G2 þ

C2G2

G2

� �1þ C1G2

þ C2G1

G2

(35)

Similarly, the overall open loop (Fig. 21) (i.e., without the VSfeedback) transfer function of the original system (without torquefeedback, C1¼ 0) is given by

HOL ¼C2G1

G2

(36)

Plotting the bode plot of these two transfer functions (Figs. 22 and23) shows that the gain margin is increased from 283 dB to323 dB (an increase by 40 dB), and phase margin is increasedfrom 85.3 deg to 137 deg (an increase by 51.7 deg). Hence, moreaggressive cruise control gains can be used when torque feedbackloop is utilized which confirms the previous observations fromsimulations of the original nonlinear model. That is an advantageon top of the better torque tracking control.

Fig. 20 Illustration of plant and controller using linearized transfer functions

Fig. 21 Overall open loop equivalent system with closed-loop feedback closing the loop onVS



8 Conclusion

All of the aforementioned challenges related to estimation ofactual delivered torque and tracking of requested torque can bepotentially addressed with a system that employs an enhancedcontroller with explicit torque feedback from the newly suggestedsensor, namely, flywheel or brake SAW torque sensor. This papershows several advantages of using such control strategy. Theadvantages include: the ability of performing torque adaption offidle, reduce pedal busyness, achieving improved and consistenttorque tracking control, and ability to utilize more aggressivecruise control gains. These advantages are enablers to better opti-mize vehicle launches and engine starts especially for enginesequipped with ESS features, potential improvements in drivelineoscillations control, as well as accomplishing better transmissionshift quality. PI controllers are designed to track both the fast andslow torques in a coordinated manner using inner–outer loopstructure within the slow path.

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Fig. 23 Bode plot of the system including inner torque controlfeedback loop

Fig. 22 Bode plot of the open loop (OL) torque control system



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Direct Torque Feedback for Accurate Engine Torque Delivery ... · torque feedback control has been proposed in the literature using either estimated or measured torques as feedback